The $1 is paid from after-tax income, so leave it as is. The $10 million is taxed, so you will only receive $7 million.With a 1 in 9 million chance of winning, the expected payoff is $7,000,000 . 1/9,000,000 + $0 .

8,999,999/9,000,000 ≈ 78 cents. Therefore, the NPV is negative for any cost of capital. If you could pay with before-tax money, the ticket would cost you only 70 cents in terms of after-tax money, so for interest rates below $0.7778/$0.70 − 1 ≈ 11.1% or so, the lottery would be a positive-NPV investment. (This assumes that you are risk neutral, on average, for such a small idiosyncratic investment.)